Abstract
The response function of a time‐varying filter changes with the output signal, or observation time. Most existing time‐varying filter techniques involve the empirical division of a seismic trace into a number of gates (or time windows) of given length, and a time‐invariant filter is determined for each such gate. Few treatments have dealt with analytical methods to establish the gate lengths according to some optimum criterion. This paper describes a technique for the determination of optimum gate lengths. It is based on the work of Berndt and Cooper, which is here applied to the calculation of time‐varying Wiener filters. The Berndt and Cooper technique produces an upper bound for the mean‐square error between the true and a given approximated time‐varying correlation function. The minimization of this upper bound leads to a relation which enables one to establish gate lengths directly from the input trace. Thereafter, ordinary time‐invariant Wiener filters can be computed for each gate. The overall filtered trace is obtained in the form of a suitably combined version of the individually filtered gates. Experimentally it is shown that, with the Berndt and Cooper technique to determine optimum gate lengths, time‐varying Wiener filters can be better than a time‐invariant filter.